I'm teaching Applied Mathematics 105a this semester. The main content of the course is complex analysis. The course is taken mainly by undergraduate students in Engineering, Physics, and Applied Mathematics. There are about 70 people in the class, which makes it the largest class I have taught in the last 10 years. I have never taught a course on complex analysis before, but have used complex analysis in my research, and have taught the method of complex variables in my graduate course on elasticity.
Michael Brenner, the Director of Undergraduate Study of the Applied Mathematics Program, introduced me to the textbook by Saff and Snider. The book costs $125.80, and gets a 4-star review on Amazon. The book is not great, but writing a textbook to please a lot of people must be a difficult thing to do. Besides, I don't know any better alternative, and am reluctant to spend time to write my own notes on the subject.
Today, I looked at several articles related to complex analysis in Wikipedia. While these articles may not replace the textbook, they are well written, and can serve as excellent supplementary readings. In particular, various hyperlinks may give better impression of the relations among topics. Here is a list of article:
- Complex number
- Function of a complex variable
- Cauchy integral theorem
- Cauchy's integral formula
- Taylor series (Intended for a real variable)
- Laurent series
- Contour integration
- Conformal mapping (This article is disappointing.)
- Fourier series (This article is much better than the section in Saff and Snider)
- Fourier transform
- Laplace transform
Daniel Suo pointed out to me a wiki that provides problems and solutions for many math courses.
I'd be curious to learn how students feel about the book by Saff and Snider. Have you found anything useful on complex analysis online? Does the cost of the book bother you, given so much is freely available online?